Question

If $ 3.0{\text{g}} $ of a salt of molecular weight $ 30 $ is dissolved in $ 250{\text{mL}} $ water. The molality of the solution is:
(A) $ 0.4 $
(B) $ 0.2 $
(C) $ 0.8 $
(D) $ 0.6 $

Answer 1

Hint: To solve this question, you must recall the formula for calculating the molality of a solution. Molality is a means of calculating the concentration of the solution, alongside many others like molarity, normality, mole fraction, etc.
 $ {\text{m}} = \dfrac{n}{{W({\text{kg}})}} $
Where, $ n $ is the number of moles of the solute present in the given solution
 $ W $ is the weight of the solvent given in kilograms
And $ m $ is the molality of the solution.

Complete step by step solution:
Concentration in simple words is the measure of the amount of solute present in the solvent, together forming a solution. Molality is also a means of calculating the concentration of the solution.
Molality is given as the number of moles of solute present per kilogram of the solvent. It is represented by “ m”. A 1 molal solution will represent a solution in which one mole of solute is dissolved in one kilogram of the solvent.
Using the data, we first find the number of moles of the solute. We know that the number of moles of a substance are given by the ratio between the given mass of the substance and its molecular/ atomic mass. We are given $ 3.0{\text{g}} $ of salt having a molecular weight of $ 30 $ . So, we can find its number of moles as $ n = \dfrac{3}{{30}} = 0.1 $
We are given the volume of the solvent (water) as $ 250{\text{mL}} $ . For calculating the molality we need the weight of the solvent. Assuming the density of water as one, we can calculate the weight of water since we know, $ \rho = \dfrac{W}{V} $
Hence, $ W = \rho .V = 250{\text{g}} $
The molality of a solution is given by $ {\text{m}} = \dfrac{n}{{W({\text{kg}})}} $ .
Substituting the values, we get, $ m = \dfrac{{0.1}}{{\dfrac{{250}}{{1000}}{\text{kg}}}} = \dfrac{{0.1 \times 1000}}{{250}} $
 $ \therefore m = 0.4 $
Thus, the correct option is option A.

Note:
It should be noted that molality is not confused with molarity. Molarity defines the concentration of a solution as the number of moles of the solute present in one liter of solution while molality defines the concentration of a solution as the number of moles of the solute present in one kilogram of the solvent.